Simplify the following expression: $x = \dfrac{n^2 + 8n - 9}{n - 1} $
Solution: First factor the polynomial in the numerator. $ n^2 + 8n - 9 = (n - 1)(n + 9) $ So we can rewrite the expression as: $x = \dfrac{(n - 1)(n + 9)}{n - 1} $ We can divide the numerator and denominator by $(n - 1)$ on condition that $n \neq 1$ Therefore $x = n + 9; n \neq 1$